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3-59.

MORE NOTABLE NOTATION FOR THE DERIVATIVE

The use ofcomes from which is an expression for slope read as "the change in*y*over the change in*x*". We use Δ to represent change. When the change gets smaller and smaller until it is infinitely small (infinitesimal) we use the symbol*d.*

It is useful to think of change when using derivatives. For examplecould represent the change in the height of an object with respect to time. Create expressions using the symbol *d*that will represent the following instantaneous change statements. Homework Help ✎The change in the velocity,

*v*, with respect to time.The change in volume,

*V,*with respect to the radius,*r,*of a cone.The change in area,

*A*, of a circle with respect to the perimeter,*p*.